Light and thermal responses of liquid-crystal-network films: A finite element study

As a polymeric system incorporating rigid molecules within its structure, the liquid-crystal network (LCN) has been envisaged as a novel heterogeneous material. Under the influence of external stimuli, the orientational order of the liquid-crystalline phase becomes dilute and overall anisotropy is hence decreased; the actinic light absorbed by photochromic molecules, for example, induces the geometric isomerization and subsequently yields internal stress within the local network. In this study we investigate light- and temperature-induced spontaneous deformations of the LCN structure via a three-dimensional finite element model that incorporates geometric nonlinearity with a photomechanical constitutive model. We first examine the bending behavior and its nonlinearity and then parametrically study the various behaviors that stem from different origins ranging from the microscale to the macroscale: (i) the geometry of the LCN film, (ii) the macroscopic global order, (iii) the distorted mesogenic orientation due to the Fredericks distortion, and (iv) defect-induced instability. These interrelated behaviors demonstrate both the simulation capability and the necessity of the presenting framework. By employing a nonlinear consideration along with a microscopic shape parameter $r$ the present approach facilitates further understanding of photomechanical physics such as the deconvolution of various stimuli and the deformed shape obtained due to snap-through instability. Furthermore, this study may offer insight into the design of light-sensitive actuation systems by deepening our knowledge and providing an efficient measure.

Figure 1

Kinematics of EICR.

Figure 2

Three-node shell formulation with 18 DOF and nematic orientation.

Figure 3

Effect of the number of integration points within a thickness on the numerical integration for midplane properties. The inset shows properties of light decay for various values of penetration depth and intensity.

Figure 4

LCN model configurations. (a) Model geometry with length, thickness, and mesogenic director $n$. (b) Depthwise angle $\varphi$ between LPL and the director. (c) Structural formula of molecules used herein (components of Azo18 [11]).

Figure 5

Curvature of the cantilevered LCN ($\mathit{n}\parallel \mathit{x}$, $h=0.5\mathrm{mm}$, $L_x=10\mathrm{mm}$, and $L_y=1\mathrm{mm}$) for various penetration depths $d$. The inset shows the changing profile of the normalized shape parameter $r/r_0$ ($y$ axis) with weaker [light gray (blue)] and stronger [dark gray (red)] light.

Figure 6

Swimming nonsquare LCN sheet under illumination for different aspect ratios $R_x/R_y$: (a) Gaussian curvature and (b) estimated strain energy scaled by a modulus.

Figure 7

Effect of director rotation on the bending direction and the emergence of twist-bend coupling.

Figure 8

(a) Evolution of the shape parameter of the twisted configuration depending on external stimuli (NPL denotes nonpolarized light and LPL linearly polarized light in the $x$ direction). (b) Ratio of principal curvatures with various external stimuli and penetration depths.

Figure 9

Shape change of the LCN sheet with radial disclination-defect-induced instability: (a) linear vs nonlinear solution, (b) instability onset, and (c) trends of critical intensity $I_{\mathrm{crit}}$ at the bifurcation point.